First, open up the lid and pop out the cup. You do this by holding onto the top and pushing up from the bottom. Ours was gross.
The tray got pretty gross too from drips. So be sure to clean that too. Nasty!
The cup that comes out breaks apart into two pieces. I cleaned both of those.
The long part that extends from the cup is where the coffee comes out. I got a toothpick and cleaned it out. You can use anything thats small enough to fit in there. If your Keurig ever gets clogged, thats where you go first.
After I reassembled the Keurig, I dumped the water tank, refilled it and ran it for a couple times without anything in it (coffee, hot chocolate, tea). A lot of dirt came out.
Thats it! Pretty simple, pretty quick too. But if you're like me and weren't sure where to start, then here you go.